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dc.contributor.authorKim, Jong Philen_US
dc.date.accessioned2007-05-25T17:47:44Z
dc.date.available2007-05-25T17:47:44Z
dc.date.issued2007-04-06en_US
dc.identifier.urihttp://hdl.handle.net/1853/14645
dc.description.abstractThe problem of constructing a confidence interval for the noncentrality parameter of a noncentral t-distribution based upon one observation from the distribution is an interesting problem with important applications. A general theoretical approach to the problem is provided by the specification and inversion of acceptance sets for each possible value of the noncentrality parameter. The standard method is based upon the arbitrary assignment of equal tail probabilities to the acceptance set, while the choices of the shortest possible acceptance sets and UMP unbiased acceptance sets provide even worse confidence intervals, which means that since the standard confidence intervals are uniformly shorter than those of UMPU method, the standard method are "biased". However, with the correct choice of acceptance sets it is possible to provide an improvement in terms of confidence interval length over the confidence intervals provided by the standard method for all values of observation. The problem of testing the equality of the noncentrality parameters of two noncentral t-distributions is considered, which naturally arises from the comparison of two signal-to-noise ratios for simple linear regression models. A test procedure is derived that is guaranteed to maintain type I error while having only minimal amounts of conservativeness, and comparisons are made with several other approaches to this problem based on variance stabilizing transformations. In summary, these simulations confirm that the new procedure has type I error probabilities that are guaranteed not to exceed the nominal level, and they demonstrate that the new procedure has size and power levels that compare well with the procedures based on variance stabilizing transformations.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectNoncentrality parametersen_US
dc.subjectTesting hypothesisen_US
dc.subjectCoefficient of variationen_US
dc.subjectSignal-to-noise ratiosen_US
dc.subjectSize of testen_US
dc.subjectPoweren_US
dc.subjectAcceptance setsen_US
dc.subjectSkewnessen_US
dc.subjectConfidence intervalen_US
dc.subjectNoncentral t-distributionsen_US
dc.titleEfficient Confidence Interval Methodologies for the Noncentrality Parameters of Noncentral T-Distributionsen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentIndustrial and Systems Engineeringen_US
dc.description.advisorCommittee Chair: Anthony J. Hayter; Committee Member: Alexander Shapiro; Committee Member: Brani Vidakovic; Committee Member: Lewis VanBrackle; Committee Member: Nicholeta Serbanen_US


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